Question

this question has two parts. first, answer part a. then, answer part b.
part a
temperature the formula ( c = \frac{wtc}{1000} ) represents the cost ( c ) in cents to operate an electrical device, where ( w ) is the wattage of the device, ( t ) is the time in hours that the device is in use, and ( c ) is the cost in cents per kilowatt-hour.
solve the formula for ( w ).
part b
if the cost to operate a device for 5 hours is $0.1875 and the cost per kilowatt hour is $0.15, find the wattage of the device.

Explanation:

Part A

Step1: Multiply both sides by 1000

To isolate the term with \( W \), we multiply both sides of the equation \( C=\frac{Wtc}{1000} \) by 1000.
\( 1000C = Wtc \)

Step2: Divide both sides by \( tc \)

Now, to solve for \( W \), we divide both sides of the equation \( 1000C = Wtc \) by \( tc \) (assuming \( t
eq0 \) and \( c
eq0 \)).
\( W=\frac{1000C}{tc} \) or \( W = \frac{1000C}{ct} \) (since multiplication is commutative, \( tc=ct \))

Step1: Convert cost to cents

The cost \( C \) is given in dollars, so we convert \( \$0.1875 \) to cents. Since \( 1\) dollar \( = 100\) cents, \( C=0.1875\times100 = 18.75 \) cents. The cost per kilowatt - hour \( c=\$0.15=0.15\times100 = 15 \) cents per kilowatt - hour, and the time \( t = 5 \) hours.

Step2: Substitute values into the formula for \( W \)

We use the formula \( W=\frac{1000C}{tc} \) from Part A. Substitute \( C = 18.75 \), \( t = 5 \), and \( c = 15 \) into the formula:
\( W=\frac{1000\times18.75}{5\times15} \)
First, calculate the numerator: \( 1000\times18.75=18750 \)
Then, calculate the denominator: \( 5\times15 = 75 \)
Now, divide the numerator by the denominator: \( W=\frac{18750}{75}=250 \)

Answer:

\( W=\frac{1000C}{tc} \)

Part B